# Tagged Questions

The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

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### Derivation of force law in special relativity

I've seen force defined in special relativity as the rate of change of 4-momentum $${\bf{F}} = \frac{d {\bf{p}}}{dt}$$ Can anyone comment on the following derivation of that relation? Take one ...
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### Twin Paradox when both twins are moving [duplicate]

Let's say twin scientists A and B start on Earth. Twin A moves east at speed v comparable to light, and Twin B moves west at speed v comparable to light. After some time, they reverse directions and ...
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### At what speeds does time dilations start to occur?

My question is, is it possible for time dilation to occur at a speed less than that of speed of light?
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### How is time dilation consistent between both observer?

There is a special variant of time dilation paradox bugs me. Imagine there are 2 small spaceships moving toward each other in constant speed. Each ship has an observer on-board. According to both ...
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### Definitions: 'locality' vs 'causality'

I'm having trouble unambiguously interpreting many answers here due to the fact that the terms locality and causality are sometimes used interchangeably, while other times seem to mean very different ...
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### Meaning and logic of Einstein's train thought experiment

This seems to be a recurrent topic but I wasn't able to find any satisfactory discussion about this tought experiment. I will quote the original story from Einstein's and put my doubts inside: Up ...
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### Einstein wrote $x^4=ict$, where $c$ is the speed of light. Does this mean the fourth dimension is moving? [closed]

Saw this on a forum: Einstein wrote$x^4=ict$, where $c$ is the speed of light. Does this mean the fourth dimension is moving? We can write $x^4=ict$ as $dx^4/dt =ic$. The fourth dimensions is thus ...
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### If one flies by the sun at .9999999c, will it become a black hole? [duplicate]

If one flies by the sun at .9999999c, will it become a black hole? If one flies by the sun at .9999999c, its width will become tiny due to relativistic contraction, while its mass will augment ...
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### Error in deriving constant acceleration relativistic distance

Bob accelerates away from Carol at proper acceleration $a$ (in light seconds per second), and Carol wants to know how far Bob has traveled when $t$ seconds pass in Bob's frame. Using ...
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### Do Einstein's postulates of relativity emerge from the Minkowski spacetime metric?

Does the constancy of the speed of light for all observers naturally emerge from the Minkowski spacetime metric? Do Einstein's two postulates of relativity emerge from the Minkowski spacetime metric? ...
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### Can $E=mc^2$ be derived from the Minkowski spacetime metric? $s^2=x^2+y^2+z^2-(ct)^2$?

Can $E=mc^2$ be derived from the Minkowski spacetime metric? $s^2=x^2+y^2+z^2-(ct)^2$? If so, how? Can the equivalence of mass and energy be derived from the Minkowski spacetime metric? Has someone ...
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### Infinitesimal transformations for a relativistic particle

The action of a free relativistic particles can be given by $$S=\frac{1}{2}\int d\tau \left(e^{-1}(\tau)g_{\mu\nu}(X)X^\mu(\tau)X^\nu(\tau)-e(\tau)m^2\right).$$ If we then make an infinitesimal ...
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### Were Michelson-Morley results a surprise?

How unexpected were the Michelson-Morley experiment results? Did physicists have theoretical reasons to predict that the speed of light would result to be invariant?
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### What's the max speed a man-made satellite can travel in space before its circuitry stopped working?

Assume it could withstand extreme temperatures in either direction. I'm mainly curious what would happen to its circuits as it approached the speed of light.
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### Radiative equilibrium of a relativistic black body

A black body in empty space in the CMB rest frame should (discounting starlight) come to an equilibrium temperature of around 2.7 K. However, if the body is moving relative to the CMB frame, one side ...
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### Force, Mass, Motion? $E = mc^2$

Does any object needs force to move? If 'yes', does the matter needs mass to form a force? These questions arises from me because $E = mc^2$ and $F = ma$ does not relate and one does not agrees with ...
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### Tensor calculus in special relativity

We say that any function $f(t,x,y,z)$ is a tensor of rank {0 0} because it takes no vectors or one-forms in order to give a real number. But couldn't we have just written the same function as ...
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### How do simple two-component Fierz identities follow from a property of the Pauli matrices?

On page 51 Peskin and Schroeder are beginning to derive basic Fierz interchange relations using two-component right-handed spinors. They start by stating the trivial (but tedious) Pauli sigma identity ...
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### Dot product in index notation [closed]

This is a question about a small exercise I am trying to do in order to check if I am correct. Such type of quantities can appear in propagators in QFT. Since I am not an index expert I need some ...
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### Different definitions of the parity transformation for the Dirac spinors

There are two definitions of the parity transformation acting on the Dirac spinors: $\Psi_P = \eta \gamma^0 \Psi$ with $\eta = i$ ($P^2=-1$ as in Srednicki) and $\eta=1$ ($P^2=+1$ as in Peskin & ...
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### Relativistic acceleration of a rocket?

I'm trying to solve a physics brain-teaser and getting nowhere fast. My knowledge of special relativity is very basic. In the problem a rocket is flying linearly at relativistic speeds (say ...
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### How does SUSY avoid to create non-Lorentz interactions?

A three-legs fermion interaction or boson absorbing a fermion are things we do not see in QFT because the corresponding terms in the Lagrangian are not Lorentz invariant. But in susy, naively, such ...
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### Gradient of $ct'$ axis in spacetime diagrams

This is either an unimportant piece of information or it's meant to be obvious, but I can't find anywhere what the gradient of the $ct'$ axis in a spacetime diagram should be. I know that the $ct'=1$ ...
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### Multiple Objects at Constant Speed

Imagine 1 million objects travelling in space, at a constant speed, along an imaginary line. They don't deviate from that line for the sake of this argument. Now, object 1 has a velocity of $v_{1}=1$ ...
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### Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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### Orthochronous Lorentz transformations are time-preserving and $SL(2,\mathbb{R})$

Let's consider the pseudosphere/hyperboloid in $\mathbb{R}^{1,2}$ given by $$x^2+y^2-z^2=-R^2.$$ We know that the Lorentz group $$O(1,2)=\{ A \in Mat(3,\mathbb{R}): A^tGA=G \},$$ where ...
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### Can the energy released from a black hole be calculated at the time of birth?

this might be a stupid question but when a black hole is formed it releases a lot of energy our satellites just catch the gamma rays and X rays released by the black hole. can we estimate the amount ...
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### What's the consensus on the block universe? Is time frozen? [duplicate]

What's the consensus view on the block universe? Is time frozen? Do the past and future exist? Was Einstein right when he said, “People like us, who believe in physics, know that the distinction ...
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### How does time dilation occur due to velocity and gravity [duplicate]

I am trying to understand and clarify the way time dilation occurs due to general and special relativity and for which reason. In the case where an object is approaching a planet in free-fall how does ...
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### Status of experimental searches for tachyons?

Now that the dust has settled on the 2011 superluminal neutrino debacle at OPERA, I'm interested in understanding the current status of experimental searches for neutrinos. Although the OPERA claim ...
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### Why did Einstein took speed of light unit or constant in his equation of relativity?

We can find that no object can have speed more than light from Einstein's equation of relativity because if anything have speed more than light then we get -ve value within square root. But why did ...
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### How to find kinetic energy given relativistic linear momentum?

The relativistic energy of a particle is given by the expression $$E^2 = m^2c^4 + p^2c^2$$ The rest energy is $E_{0}=mc^2$ and the momentum is $p=mc$. In the rest frame, ...
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### How do I derive the Lorentz contraction from the invariant interval?

Reviewing some basic special relativity, and I stumbled upon this problem: From the definition of the proper time: $$c^2d\tau^2=c^2dt^2-dx^2$$ I was able to derive the time dilation formula by using ...
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### Mass and frequency of photons [duplicate]

Light is affected by gravity which means light has got mass. Quantum theory tells us that light consists of discrete quanta of energy, which we call photons. These photons have a rest mass of zero (as ...